1) An alpha particle is a helium nucleus that consists of two protons bound with
ID: 2121447 • Letter: 1
Question
1) An alpha particle is a helium nucleus that consists of two protons bound with two neutrons. An alpha particle moving through a perpendicular magnetic field of 1.6 T experiences an acceleration of 1820 m/s2. What is the alpha particle's speed?
2) An electron has an initial velocity B when it enters a region in which is parallel to the z direction (see the figure below). If vB = 580 m/s and B = 0.77 T, what is the radius of the trajectory?
3)Four very long wires are directed perpendicular to the plane of the figure below. The points where these wires cross the plane of the drawing form a square of edge length 0.38 m, and each wire carries a current of magnitude 2.9 A. Find the magnetic field at the center of the square (i.e., at the origin).
Explanation / Answer
1) q = 1.6*10^-19 c
m = 4*1.67*10^-27 kg = 6.68*10^-27 kg
a = 1820 m/s^2
F = q*v*B
m*a = q*v*B
===> v = m*a/B*q = 2.4*10^-5 m/s
2) me = 9.1*10^-31 kf, qe = 1.6*10^-19 c
v = 580 m/s, B=0.77 T
m*v^2/r = q*v*B
r = m*v/B*q = 4.2888*10^-9 m
3)
diagonal of the square d = sqrt(0.38^2 + 0.38^2) = 0.54 m
distance from each wire r = 0.54/2 = 0.27 m
all the magnitudes are same
B1 = B2 =B3 =B4 = B = mue*i/(2*pi*r) = 2.148*10^-6 T
B1 and B3 are parallel, so B13 = 4.296*10^-6 T
B2 and B4 are parallel, so B24 = 4.296*10^-6 T
but B13 and B24 are perpendicular
Bnet = sqrt(B13^2 + B24^2) = 6.075*10^-6 T (towards -y-axis)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.